Arithmetical rank of the edge ideals of some \(n^-\) cyclic graphs with a common vertex. (Chinese. English summary) Zbl 1349.05209
Summary: In this paper, we obtain some lower bounds and upper bounds on the arithmetical rank of the edge ideals of some \(n^-\) cyclic graphs with a common vertex. For some special \(n^-\) cyclic graphs, we prove that their arithmetical ranks equal the projective dimension of the corresponding quotient ring.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 15A03 | Vector spaces, linear dependence, rank, lineability |
| 13C10 | Projective and free modules and ideals in commutative rings |
| 13C15 | Dimension theory, depth, related commutative rings (catenary, etc.) |
